1726 LETTER Blind Fake Image Detection Scheme Using SVD

1726IEICE MUN.,VOL.E89–B,NO.5MAY2006LETTERBlind Fake Image Detection Scheme Using SVDWei LU†a),Fu-Lai CHUNG††b),and Hongtao LU†c),NonmembersSUMMARY The release of image processing techniques make image modification and fakery easier.Image fakery,here,is defined as a process to copy a region of source image and paste it onto the destination image, with some post processing methods applied,such as boundary smoothing, blurring,etc.to make it natural.The most important characteristic of image fakery is object copy and paste.In order to detect fake images,this letter introduces a blind detection scheme based on singular value decomposition (SVD).Experimental results also show the effectiveness of the proposed scheme.key words:fake image detection,singular value decomposition1.IntroductionWith the development of digital image processing technol-ogy and the popularization of image processing programs, such as Photoshop,GIMP etc.,image fakery is becoming easier than before.Many fake images can be found on Inter-net.Most fake images are made through a process of object copy and paste,where some image processing techniques are used to make fake image natural in signal characteris-tics,but most of the fake images are irrational and illogical on their contents.From the website[1],one mayfind an example of the fake images,where the face of Andy Lau,a Hong Kong super star,is pasted onto a still photograph of the famous movie,The Lord of the Rings.It is still a problem how to detect whether digital im-ages are fake or real.Generally,there is an obvious bound-ary between the fake area and the real area,with the im-provement of desktop photograph manipulation software, which can not be used to distinguish fake images and real images.In[2],a blind detection of photomontage is intro-duced using higher order statistics,where photomontage is a similar concept with image fakery.In[3],a model based on bipolar signal perturbation is introduced to detect spliced images.These two papers used a statistics model and bico-herence features to detect image forgery,and they are often used to detect human speech signal.In[4],Popescu and Farid introduced some techniques of exposing digital forg-Manuscript received October19,2005.Manuscript revised December2,2005.†The authors are with the Department of Computer Sci-ence and Engineering,Shanghai Jiao Tong University,Shanghai 200030,China.††The author is with the Department of Computing,Hong Kong Polytechnic University,Hung Hom,Kowloon,Hong Kong.a)E-mail:luweicn@b)E-mail:cskchung@.hkc)E-mail:lu-ht@DOI:10.1093/ietcom/e89–b.5.1726eries by detecting traces of resampling,which also tried to resolve the similar problem.In this letter,a SVD based fake image detection scheme is developed,which uses the change of the direction of the eigenvector in orthogonal subspace to detect the evidence of image fakery.Experiments show that the proposed scheme works well and the results are encouraging.2.Image PreprocessingBefore the original image is open to public,preprocessing is applied to make an assistant for the following fake de-tection.Singular value decomposition is known as a signal processing technique to diagonalize a matrix,and the diag-onal elements are also stable under modification of matrix signal[5].First the original image I is transformed using SVD:I=US V T(1) where U and V are the orthogonal matrices,V T denotes the transpose of V,and S is a diagonal matrix,whose diago-nal elements can form a column vector v.Then two se-cret column vectors,v1,v2are constructed,and they satisfy v1·v =0, v2·v =0and v1·v2 =0,where‘·’denotes theinner product.Then the following equation is computed: v =v+αv1vv1 (2) whereαis a scalar factor,which is set to0.01in our experi-ments.The vector v is restored to the diagonal elements of zero matrix S correspondingly,a new image I is obtained using the following equation:I =US V T(3) which is the preprocessed image and open to public.As is known,SVD is robust to slight perturbation of images,i.e., the vector v is stable under slight alteration of the image.In our image preprocessing procedure,the perturbation to the vector v in Eq.(2)is small,i.e.,v ≈v,so the image prepro-cessing does not decrease the quality of original images too much,which will be demonstrated in the later experiments.3.The Proposed Fake Detection SchemeFor an input test image I∗for fake detection,similarly it is decomposed using SVD as follow:Copyright c 2006The Institute of Electronics,Information and Communication EngineersLETTER1727I ∗=U ∗S ∗(V ∗)T(4)Then the column vector v ∗is obtained from the diagonal el-ements of S ∗.The proposed fake image detection can be given as follow:ρ= v ∗ v ∗ ·v 1 v 1 + v ∗ v ∗ ·v 2 v 2 (5)where ρis the detection value,which denotes the fake de-gree of the test image.Here,a threshold T th is set,if ρ≥T th ,we can conclude that the input image is fake,otherwise it is not fake.In the proposed scheme,the two secret vectors,v 1and v 2,are the key construction,on which the detection result depends.Suppose v = v 1 = v 2 and v ∗=v +v f ,i.e.,the vector v ∗is composed of two vectors,one is the original vector v ,the other is the fake vector v f .Also,we have v =v +αv 1 v v 1 ,thusρ= v +v f v ∗ ·v 1 v 1 + v +v f v ∗ ·v 2 v 2= (v f +v +αv 1 v v 1 )·(v 1+v 2) v ∗ v 2 (6)Based on the orthogonal relation among v ,v 1and v 2,we have ρ= v f ·(v 1+v 2)+αv 1·v 1 v v 1 v ∗ v 2 (7)Here,the scalar factor αis small enough,and the equationabove can be computed approximately as follow:ρ≈ v f ·(v 1+v 2) v ∗ v 2=v f v 1+v 2 v ∗ v 2 =√2 v fv ∗ (8)It is obvious that the detection result ρdepends on thevector v f ,while v f denotes the fake degree of the tested im-age,so the detection value ρcan reflect that whether the input image is fake.Also,there are two secret vectors in our proposed process,v 1and v 2,which do not have influence on the absolute value of detection result.4.Results and DiscussionsSome experiments were carried out to test the proposed fake image detection scheme.Firstly,1000test images are used,and they are divided into two classes.One is 500real im-ages,and the other is 500fake images which are created using the 500real images by altering proper areas.A pair of examples are shown in Fig.1,where Fig.1(a)is the real image and Fig.1(b)is the fake image.Figure 2shows the histogram response of the detection results ρfor these 1000tested images.It is obvious that the response for the two classes of images are clear.Based on Fig.2,when T this(a)(b)Fig.1(a)The open image after preprocessing.(b)A fake version of(a).Fig.2The histogram response of ρfor 500real images and 500fake images.set to 0.01,the detection threshold can distinguish the two classes of images correctly.Because of the introduction of image preprocessing,the distortions to original images are unavoidable.We also test the similarity between the original images and the open images using Peak Signal-to-Noise Ratio (PSNR)which is a common measure of signal distortions.The result shows that all the PSNR of the test images are larger than 36,and PSNR =38.2for the Lenna image in Fig.1.So,we consider that the distortions introduced by image preprocessing can be ignored.Based on Eq.(8),the detection result depends on the fake vector v f ,so a slight fakery will result in a small detec-tion result,while a significant fakery will result in a large detection result.In order to further test the performance of the proposed scheme,a image database of 2000images is also used,and the fake images are created using objects with di fferent size.Figure 3gives the ROC curve between the false positive rate and the true positive rate based on the di fferent threshold T th ,where the false positive rate is the percentage of real images that are incorrectly determined as fake images,and the true positive rate is the percentage of fake images that are correctly determined as fake images.When T th =0.01,the false positive rate is 0.8%and the true1728IEICE MUN.,VOL.E89–B,NO.5MAY2006Fig.3The ROC curve between the false positive rate and the true posi-tive rate.positive rate is 86.7%.By analyzing the relation between the images and the detection results,we found that the false negative detection mostly concentrates on the images with small fake area,so it can be concluded that the proposed de-tector becomes more sensitive with smaller fake area,and it is partially due to the robustness of SVD.5.ConclusionsIn this letter,we have proposed a SVD based fake image de-tection scheme.Before the images are open to public,some assistant information is inserted into them.Recurring tothe secret information,we can make a decision on whether test images are fake or not using the proposed SVD based detection scheme.Experimental results also show that the proposed fake image detection scheme is e ffective.Future research is to achieve a performance enhanced SVD based fake image detection scheme combined with vector space orthogonal decomposition and classification using support vector machine.AcknowledgmentsThis work is supported by NSFC under project no.60573033and the PolyU ICRG grant under project A-PG49.The authors would like to thank the reviewers for their help-ful suggestions and comments,which improved the final version of this paper.References[1] /news /shownews.asp?NewsID =2540[2]T.T.Ng,S.F.Chang,and Q.Sun,“Blind detection of photomontageusing higher order statistics,”IEEE Int.Symp.Circuits Syst.(ISCAS),pp.688–691,May 2004.[3]T.T.Ng and S.F.Chang,“A model for image splicing,”IEEE Int.Conf.Image Process.(ICIP),pp.1169–1172,Oct.2004.[4] A.C.Popescu and H.Farid,“Exposing digital forgeries by detect-ing traces of resampling,”IEEE Trans.Signal Process.,vol.53,no.2,pp.758–767,Feb.2005.[5]H.Andrews and C.Patterson,“Singular value decompositions anddigital image processing,”IEEE Trans.Acoust.Speech Signal Pro-cess.,vol.24,no.1,pp.26–53,Feb.1976.。